Question

a cuboid-shaped container which is three-quarters filled with water is shown below.

how much extra water, in litres, would be needed to completely fill the tank?

\\1\text{ cm}^3 = 1\text{ ml}\\

Explanation:

⚡ Using what you learned: calculating volume of rectangular prisms · Unit Conversion (metric and customary)

Step 1: Calculate total volume of the cuboid

The dimensions of the cuboid are \(1\text{ m}\), \(3\text{ m}\), and \(4\text{ m}\).

$$ V_{\text{total}} = 1\text{ m} \times 3\text{ m} \times 4\text{ m} = 12\text{ m}^3 $$

Step 2: Determine the volume of extra water needed

The container is three-quarters (\(\frac{3}{4}\)) full, so the remaining empty space is one-quarter (\(\frac{1}{4}\)) of the total volume.

$$ V_{\text{needed}} = \frac{1}{4} \times 12\text{ m}^3 = 3\text{ m}^3 $$

Step 3: Convert the volume to litres

First, convert cubic meters to cubic centimeters:

$$ 1\text{ m} = 100\text{ cm} $$

$$ 1\text{ m}^3 = (100\text{ cm})^3 = 1,000,000\text{ cm}^3 $$

$$ 3\text{ m}^3 = 3 \times 1,000,000\text{ cm}^3 = 3,000,000\text{ cm}^3 $$

Using the conversion \(1\text{ cm}^3 = 1\text{ ml}\):

$$ 3,000,000\text{ cm}^3 = 3,000,000\text{ ml} $$

Convert milliliters to litres (\(1\text{ L} = 1000\text{ ml}\)):

$$ \frac{3,000,000\text{ ml}}{1000} = 3000\text{ L} $$

Answer:

3000